It would work just fine.
But (assuming it's a 12V battery) you'll get twice the charging current if you reconnect the panels in parallel.
With the seriesed panels you'll get the same charging current as if you had fewer panels in series or lower voltage panels (down to where you have only enough extra open-circuit volts above your battery voltage to cover resistive losses and panel voltage reduction from high panel temperature).
Solar panels are essentially current limited devices. As long as your panel voltage is sufficiently above the battery voltage that it is the panel's current output that limits the charging current (rather than voltage drop in the panels' wiring resistance) the charging current will be the same no matter how many panels are in series. The number of electrons you get is limited by the number of photons striking the least illuminated (parallel set of) cell(s).
The extra energy is dissipated as heat in the panel. It's not an issue, since completely shorting the panel or array causes its total heating to be the same as leaving it out in the sun unconnected to anything. Pulling any power at all reduces the heating by the amount of energy you pulled. Solar regulators generally prevent overcharging by shorting the panel out. The anti-backflow diode keeps the battery from discharging into the short the regulator applies.
Does anyone know if a 17.5 Ah SLA can recombine hydrogen and oxygen fast enough to handle 150 milliamps of overcharge trickle current? If not you'll need some way to protect them from overcharging.
(Fortunately there's little enough power to dissipate that you could just hang a 2W zener at your float voltage across your battery as a dump load - or a couple of 1W zeners in series at half the float voltage. Double the power rating if you decide to parallel the panels.)
